To the best of my understanding, by the mid fifties the 1600 lb AP had been phased out of service, so the issue of the conical fin assembly is not relevant for this bomb.
The 2000lb SAP would be phased out by the end of the same decade. However these bombs kept appearing in bombs related documents as "obsolete" are the stocks were not still completely emptied - and this still the mid sixties.
The 1000 lb AN-M59A2 seems to have been the only SAP to be still in service by the mid sixties, still equipped with a ww2 box-type in.
It must be well understood that the conical fin assembly was defined as an "intermediary" stage, designed to enable the use of existing stocks of ww2-era bombs in the mid-/late fifties till their replacement by "modern bombs" - the M117 / M118/ M121 and the Mk 80/81/82/83/84 series.
These conical fin assemblies were in fact specifically designed for the GP bombs - here's a timetable of their development with establishement of the suited bombing tables
Bombing Table for 100-lb. G.P. Bomb AN-M30A1 with Fin Assembly M135 1/2/1955
Bombing Table for 250-lb. G.P. Bomb AN-M57A1 with Fin Assembly M126 13/1/1954
Bombing Table for 500-lb. G.P. Bomb AN-M64A1 with Fin Assembly M128 19/1/1954
Bombing Table for 1000-lb. G.P. Bomb AN-M65A1 with Fin Assembly M129 23/7/1957
Bombing Table for 2000-lb. G.P. Bomb AN-M66A2 with Fin Assembly AN-M116A1 or M116 4/2/1952
The following tables give the various assemblies (box and conical) possible for US bombs during this intermediary period (As it is a Navy documents, it includes Navy bombs - a peculiarity ingerited from teh interwar period, that was not entirely superseded by the AN series, but will disappear with the "modern" bomb series that will finally unify the US air-dropped arsenal.)
Hope this helps.